Geodesic
On the continuous analogue of the Seidel method
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 4, pp. 364-377

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Continuous Seidel method for solving systems of linear and nonlinear algebraic equations is constructed in the article, and the convergence of this method is investigated. According to the method discussed, solving a system of algebraic equations is reduced to solving systems of ordinary differential equations with delay. This allows to use rich arsenal of numerical ODE solution methods while solving systems of algebraic equations. The main advantage of the continuous analogue of the Seidel method compared to the classical one is that it does not require all the elements of the diagonal matrix to be non-zero while solving linear algebraic equations’ systems. The continuous analogue has the similar advantage when solving systems of nonlinear equations.
Keywords: systems of algebraic equations, Seidel method, systems of ordinary differential equations, delay. 
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     author = {I. V. Boykov and A. I. Boikova},
     title = {On the continuous analogue of the {Seidel} method},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
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I. V. Boykov; A. I. Boikova. On the continuous analogue of the Seidel method. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 4, pp. 364-377. http://geodesic.mathdoc.fr/item/SVMO_2018_20_4_a0/